Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization

Abstract

We study focussing discrete nonlinear Schrödinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and provides the existence of two one-parameter families of waves with unimodal and even profile function for a wide class of nonlinearities. Finally, we illustrate our results by numerical simulations.

new version with revised introduction and improved condition (A3); 16 pages, several figures

References in corpus (2)

• Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation
• Heteroclinic standing waves in defocussing DNLS equations -- Variational approach via energy minimization

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